The branching problem asks how a given irreducible representation of a group decomposes when restricted to a subgroup.Making an observation on wild features of branching problems for non-compact subgroups in the general setting, we address the question of finding a criterion for discreteness of spectrum and finiteness of multiplicities in the irreducible decomposition of the restriction.
We also will indicate some applications of our theorems to topological results on modular varieties in locally symmetric spaces, and construction of new discrete series representations for pseudo-Riemannian homogeneous spaces.
© Toshiyuki Kobayashi